Complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm

Abstract

In this paper, two equivalent definitions of complex strongly extreme points in general complex Banach spaces are shown. It is proved that for any Orlicz sequence space equipped with the p-Amemiya norm (1 p < ∞, p is odd), complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in Orlicz sequence spaces equipped with the p-Amemiya norm are given. Criteria for complex mid-point locally uniform rotundity and complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm are also deduced.

Complex Convexity of Orlicz Modular Sequence Spaces

“…In [34], we have given criteria for complex strict convexity and complex midpoint locally uniform convexity of Orlicz sequence spaces equipped with the -Amemiya norm.…”

Uniform rotundity of Orlicz function spaces equipped with the ‐Amemiya norm

“…not only in the case when Φ is an N‐function) and that the Luxemburg norm and ∞‐Amemiya norm coincide (see ). Since that time, an intensive development of research connected with Orlicz and Musielak–Orlicz spaces equipped with the p‐Amemiya norm has taken place, many important results broaden the knowledge about the geometry of these spaces were obtained (see ) and some open questions were put .…”